Question

i) Indicate all the 3NF violations.

ii) Decompose the relations, as necessary, into collections of relations that are in 3NF.

a) R(A,B,C,D) with FD's AB --> C, C --> D, and D --> A.

f) R(A,B,C,D,E) with FD's AB --> C, C --> D, D --> B, and D --> E.

Answer 1

1)3NF Violation -

• Spot/Find a functional dependency X → B such that: B is a non-key attribute (i.e., not part of any key), and. X is not a superkey.
• Relation should satisfy 2NF condition
• Every non-key attribute is non-transitively dependent on all the keys
• Transitive function dependency : A function dependency A --> B is a transitive function dependency if their is a X which is A->X and X->B and X should no be a SUPER Key . if X is a superkey in relation R , then 3NF is not violated !!!

2)

a)R(A,B,C,D) with FD's AB --> C, C --> D, and D --> A.

C --> D and D --> A.

so we can write C --> A and D should not be super key

AB --> C and we got C --> A so we can write AB --> A where C should not be super key.

f) R(A,B,C,D,E) with FD's AB --> C, C --> D, D --> B, and D --> E.

form C --> D, D --> B we can say C --> B and D should not be a Super key

from C --> D, and D --> E we can say C --> E and D should not be a Super key

and from AB --> C and above C --> B and C --> E

we can write AB --> B or AB --> E